Increasing sophistication of brain recording technology has not been matched by a similarly sophisticated mathematical approach that permits modeling and prediction of the relation between behavior and the activity of populations of cells deep within the nervous system. This is particularly true for motor systems, where the primary goal is control of the dynamics of the environment. Our goal is to create multiscale models of motor components of the spinal cord that can link at least four scales: (1) individual neuron firing, (2) local neural population activity, (3) topographic maps of activity across the spinal cord, and (4) behavior. We propose to use the spinalized frog as our testbed, because the biomechanics are well understood, proprioceptive feedback is simplified, the cord can be studied in isolation from cortical control, and repeatable complex movements can be generated in the absence of cortical control. We will use and further develop a new mathematical framework based upon superposition of stochastic dynamic operators. It is appropriate to consider neural activity as causing a modification of the system dynamics, so that the resulting dynamics (including movement, compliance, and oscillatory behavior) achieve a desired result. The new framework allows us to model the response to dynamic environments, compliant control, reflex behavior, the effect of single spikes, and the combined effect of multiple neurons in a population. We can examine oscillatory activity (such as found in the central pattern generator (CPG) for locomotion) and the role of proprioceptive feedback. Because this theory operates at the level of single spikes and all neural representations are local and can use local learning rules, it provides a much closer link to the actual biological computations and could provide insight into the mechanisms used by the spinal cord to generate complex and varied movement. To test our understanding of the behavior of populations of neurons in the intermediate layers of spinal cord, we will (1) read out the dynamics of ongoing movement including perturbation responses and compliance, (2) modify the dynamics of ongoing movement, (3) create topographic maps showing the distribution of control functions across the cord. These experiments will allow us to understand control by neural populations of the dynamics of movement in a detailed way that links the neural scale to the population scale to the motor behavioral scale. The mathematical framework provides a new model for understanding the function of populations of neurons and predicting their effect on behavior. It also provides a quantitative model that allows the prediction of the effect of modification of firig or injury on behavior. Finally, it will provide the basis for new treatments for spinal cord injuryby giving an understanding of functional electrical stimulation that can be used not just to generate forces in target muscles, but can be used to generate smooth compliant control of dynamics in the way naturally used by the body.